Anamorphosis is defined as the stretching of images but not otherwise blurring them. In many cases, this is done intentionally to achieve aesthetic or technical advantages. However, the natural occurrence of anamorphosis can be problematic. For example, an underwater “viewer” looking up out of the water sees the whole half-sphere (above the water's surface) in principle, but sees it in a highly distorted manner. The change of media from air to water makes everything appear to occupy a smaller angle. Even images at the viewer's zenith are smaller than they would appear than if the transmission medium were uniform. Thus, the underwater viewer sees the horizon-to-horizon out-of-water world confined to a broad cone. The dimensions of this cone can be calculated using Snell's Law. In general, if θincident is the horizon angle of incidence and θexiting is the horizon angle of exit, then Snell's Law can be written as nincident cos(θincident)=nexiting cos(θexiting),
where nincident is the refraction index of the medium before the ray is incident on the interface and nexiting is the refractive index of the medium after the ray exits the interface. For example, if nincident is 1.0 (i.e., the approximate index of air), nexiting is 1.34 (i.e., the approximate index of seawater), and θincident is 0 degrees (i.e., light coming from the horizon), then θexiting is 41.73 degrees. Thus, all of the light that an underwater viewer sees appears to be coming from between 41.73 degrees from the viewer's horizon to the viewer's zenith.
As the underwater viewer's field of view approaches the air horizon, objects appear more and more compressed vertically relative to their horizontal extent. For a square object 10 degrees above the horizon, its underwater aspect appears compressed to a height only one-fourth of its length. This anamorphic compression is objectionable to a viewer of a scene.